The news that France has begun supplying arms to Libyan rebels is likely to deepen discord within the NATO alliance, which is in charge of the 103-day Western military campaign, but has refrained from giving direct support to the rebels given that the mission was authorized by a U.N. Security Council resolution aimed at protecting Libya’s civilians. While the French deem arming the rebels as permissible within the bounds of the U.N. resolution, many other interested parties, within NATO and outside, regard it as a violation of that resolution’s arms embargo. But such legal niceties are of secondary importance; the bigger problem facing the NATO effort is that the European alliance members who have undertaken most of the combat over Libya near the limits of the resources they can devote to expeditionary warfare. And the U.S. is highly unlikely, given the level of opposition on Capitol Hill to even the current limited support role, to fill the breach. Pressure is growing within the alliance and outside of it to end the military campaign and seek a political solution to the crisis, with the bombing campaign having weakened the regime but not broken it.

Calls for a cease-fire are now coming from key players in the alliance, including Italy (the only country from whose territory air sorties are being flown — most of the combat missions are flown from the French aircraft carrier Charles De Gaulle, which is be rotated out of the theater in September, with no obvious replacement) and Turkey — on whom the alliance will depend to supply any ground forces needed to police a post-conflict situation. Their preference for a political solution now is shared by the African Union and the Arab League, whose political support was vital to enable a third Western military campaign in a Muslim country within the space of decade.

Regardless of when the fighting stops, it has become increasingly clear that the political solution demanded by NATO will involve some form of interim power-sharing between rebels and elements of the old regime, rather than installing the Benghazi-based rebel leadership the new rulers in Tripoli. On one hand, that’s the inevitable consequence of the regime’s survival of NATO’s air war, and he fact that the alliance has no intention of launching a ground invasion. But it may actually be viewed in Western capitals as the more desirable outcome so as to avoid repeating the mistakes of the U.S.-led invasions of Afghanistan and Iraq.

The British government effectively said as much in in a document presented to the rebel Transitional National Council leadership in Benghazi, calling for a “politically inclusive settlement” to avoid repeating mistakes made by the U.S. in Iraq. Britain’s International Development Secretary Andrew Mitchell this week stressed “the importance of using to the maximum possible extent existing structures” when it comes to security in a post-conflict Libya. In other words, he made clear, don’t expect a wholesale dismantling of the old regime police and army: “One of the first things that should happen once Tripoli falls is that someone should get on the phone to the former Tripoli chief of police and tell him he’s got a job and he needs to ensure the safety and security of the people of Tripoli,” Mitchell said Tuesday at a press conference announcing the recommendations his government had made to Benghazi. He also made clear that the U.K. and its partners would have major input into decision making, given their central role in the war effort. The rebels are simply unable to topple Gaddafi and set up an alternative regime without Western backing, which means the Western powers are in a stronger position to set limits on the rebels’ ambitions.

The British report also made clear that were international peacekeeping troops required – a strong possibility – they would not come from the U.K. (or likely from any other European NATO member) but that Turkey would be the most likely to play sheriff. And Turkey has all along favored a political solution that integrates as much as possible of Libyan society, including the old regime, into a new democratic political order.

Last week, the rebels admitted holding indirect talks with the regime, and although they insist on Gaddafi stepping aside, rebel spokesmen have raised the possibility of his moving to a remote location inside Libya to see out his days. The ICC warrant for his arrest might complicate that, although it doesn’t alter the underlying political logic of that option — the rebels, after all, are a lot more versed in the crimes of the Colonel than the prosecutors at the Hague are. And with Libya not being a signatory to the treaty that established the court, it would be under no legal obligation to turn him over.

Fighting on the ground is likely to intensify in the days and weeks ahead, however, if for no other reason than the awareness of the combatants that NATO’s timetable may not extend beyond the summer.

Tony Karon is a senior editor at TIME, where he has covered international conflicts in the Middle East, Asia, and the Balkans since 1997. A native of South Africa, he now resides with his family in Brooklyn, New York.